There are two basic techniques used in digital-to-analog converters (DACs). These are the sigma-delta technique and the resistive or capacitive divider techniques. The sigma-delta technique is attractive because it achieves high resolution by precise timing instead of precisely-matched on-chip components such as resistors. In addition, the expertise needed to produce thin-film, laser-trimmed analog components is difficult to obtain; whereas, high-speed digital switching capability is commonplace in the semiconductor industry.
A basic sigma-delta DAC receives a digital signal which is summed with inverse feedback of the analog output signal (after being reconverted to a digital signal) to provide an error signal. The error signal is then processed through an integrator and a comparator to provide the analog output signal. The analog signal is also processed through an analog-to-digital converter (ADC) to provide the feedback signal.
Sigma-delta modulators with orders greater than one (and often with orders equal to one) do not operate on a full scale signal. These sigma-delta modulators typically give up 1-2 decibles (dB) of dynamic range in exchange for being able to randomize and shape the quantization error out of band. However, this performance is disastrous when the DAC receives full-scale signals. Known DACs have solved this problem by either by clipping input data words, or by adding a fast impulse response (FIR) filter whose coefficients attenuate the digital signal, or by multiplying data input words by a fixed amplitude factor. Clipping input data words hurts performance, while the latter two approaches increase system cost. New, less costly ways of processing full scale input signals are needed.
Ledzius and Irwin in U.S. Pat. No. 5,057,840 teach a sufficiently resolved sigma-delta modulator in which a most significant or coarse bit and at least one less significant or trim bit are used as feedback bits. By including the trim bit in the feedback path, the sufficiently-resolved sigma-delta modulator improves the signal-to-noise ratio for small input signals. However, the use of the trim bit or bits in the feedback path causes the idle or higher frequency out-of-band duty cycle point to be somewhat different from a half-scale signal.